18-误差逆向传播的代码实现.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "向量化运算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div  align=\"center\">    \n",
    "     <img src = './img/34.jpg', width=600, height=200/>\n",
    "     <img src = './img/35.jpg', width=600, height=200/>\n",
    "     <img src = './img/36.jpg', width=600, height=200/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "#coding=utf-8\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import random\n",
    " \n",
    "class NeuralNetwork(object):\n",
    "    def __init__(self, sizes, act, act_derivative, cost_derivative):\n",
    "        #sizes表示神经网络各层的神经元个数，第一层为输入层，最后一层为输出层\n",
    "        #act为神经元的激活函数\n",
    "        #act_derivative为激活函数的导数\n",
    "        #cost_derivative为损失函数的导数\n",
    "        self.num_layers = len(sizes)\n",
    "        self.sizes = sizes\n",
    "        self.biases = [np.random.randn(nueron_num, 1) for nueron_num in sizes[1:]]\n",
    "        self.weights = [np.random.randn(next_layer_nueron_num, nueron_num)\n",
    "            for nueron_num, next_layer_nueron_num in zip(sizes[:-1], sizes[1:])]\n",
    "        self.act=act\n",
    "        self.act_derivative=act_derivative\n",
    "        self.cost_derivative=cost_derivative\n",
    "        self._w = None\n",
    "        self._g = None\n",
    "        self._predict = None\n",
    " \n",
    "    #正向传播,计算输出的结果啦\n",
    "    def feedforward(self, a):\n",
    "        for b, w in zip(self.biases, self.weights):\n",
    "            a = self.act(np.dot(w, a)+b)\n",
    "        return a\n",
    " \n",
    "    #批量随机梯度下降算法\n",
    "    def SGD(self, training_data, epochs, batch_size, learning_rate, y_true):\n",
    "        #将训练样本training_data随机分为若干个长度为batch_size的batch\n",
    "        #使用各个batch的数据不断调整参数，学习率为learning_rate\n",
    "        #迭代epochs次\n",
    "        n = len(training_data)\n",
    "        for j in range(epochs):\n",
    "            random.shuffle(training_data)\n",
    "            # 进行数据的分割\n",
    "            batches = [training_data[k:k+batch_size] for k in range(0, n, batch_size)]\n",
    "            for batch in batches:\n",
    "                # 接收更新完成的参数，进行打印\n",
    "                weight_last, biase_last = self.update_batch(batch, learning_rate)\n",
    "            print(\"Epoch {0} complete, total errors is {1}\".format(j, np.sum((y_true.T-self._predict)**2)))\n",
    "            \n",
    " \n",
    "    def update_batch(self, batch, learning_rate):\n",
    "        #根据一个batch中的训练样本，调整各个参数值\n",
    "        nabla_b = [np.zeros(b.shape) for b in self.biases]\n",
    "        nabla_w = [np.zeros(w.shape) for w in self.weights]\n",
    "        for x, y in batch:\n",
    "            delta_nabla_b, delta_nabla_w = self.backprop(x, y)\n",
    "            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]\n",
    "            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]\n",
    "        #计算梯度，并调整各个参数值\n",
    "        self.weights = [w-(learning_rate/len(batch))*nw for w, nw in zip(self.weights, nabla_w)]\n",
    "        self.biases = [b-(learning_rate/len(batch))*nb for b, nb in zip(self.biases, nabla_b)]\n",
    "        return self.weights[-1], self.biases[-1]\n",
    " \n",
    "    #反向传播（重点）\n",
    "    def backprop(self, x, y):\n",
    "        #保存b和w的偏导数值\n",
    "        nabla_g = [np.zeros(b.shape) for b in self.biases]\n",
    "        nabla_w = [np.zeros(w.shape) for w in self.weights]\n",
    "        #正向传播\n",
    "        activation = x\n",
    "        #保存每一层神经输出值\n",
    "        activations = [x]\n",
    "        #保存每一层神经输入值\n",
    "        zs = []\n",
    "        for b, w in zip(self.biases, self.weights):\n",
    "            z = np.dot(w, activation)+b\n",
    "            zs.append(z)\n",
    "            activation = self.act(z)\n",
    "            activations.append(activation)\n",
    "        self._predict = np.array(activations[-1][0]).reshape(-1, 1)\n",
    "        #反向传播得到各个参数的偏导数值\n",
    "        g = self.cost_derivative(activations[-1], y) * self.act_derivative(zs[-1])\n",
    "        nabla_g[-1] = g\n",
    "        nabla_w[-1] = np.dot(g, activations[-2].transpose())\n",
    "        #反向逐层计算\n",
    "        for l in range(2, self.num_layers):\n",
    "            z = zs[-l]\n",
    "            sp = self.act_derivative(z)\n",
    "            #反向逐层求参数偏导\n",
    "            g = np.dot(self.weights[-l+1].transpose(), g) * sp\n",
    "            nabla_g[-l] = g\n",
    "            nabla_w[-l] = np.dot(g, activations[-l-1].transpose())\n",
    "        return (nabla_g, nabla_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 损失函数的偏导数\n",
    "def cost_derivative(output_activations, y):\n",
    "    return 2*(output_activations-y)\n",
    " \n",
    "# sigmoid函数\n",
    "def sigmoid(z):\n",
    "    return 1.0/(1.0+np.exp(-z))\n",
    " \n",
    "# sigmoid函数的导数\n",
    "def sigmoid_derivative(z):\n",
    "    return sigmoid(z)*(1-sigmoid(z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 complete, total errors is 30.20551440201369\n",
      "Epoch 1 complete, total errors is 26.926971266682735\n",
      "Epoch 2 complete, total errors is 27.724946229859235\n",
      "Epoch 3 complete, total errors is 27.715262697206505\n",
      "Epoch 4 complete, total errors is 26.613734538031906\n",
      "Epoch 5 complete, total errors is 26.32403977796019\n",
      "Epoch 6 complete, total errors is 27.018054955038515\n",
      "Epoch 7 complete, total errors is 26.794262790677653\n",
      "Epoch 8 complete, total errors is 26.372081853024522\n",
      "Epoch 9 complete, total errors is 26.782767420193057\n",
      "Epoch 10 complete, total errors is 26.548696305066553\n",
      "Epoch 11 complete, total errors is 26.305325325306278\n",
      "Epoch 12 complete, total errors is 26.51838830033944\n",
      "Epoch 13 complete, total errors is 26.46832448040494\n",
      "Epoch 14 complete, total errors is 26.39580390776873\n",
      "Epoch 15 complete, total errors is 26.84705600211057\n",
      "Epoch 16 complete, total errors is 26.382161570214105\n",
      "Epoch 17 complete, total errors is 26.42659983287196\n",
      "Epoch 18 complete, total errors is 26.39807550347285\n",
      "Epoch 19 complete, total errors is 26.36294442515676\n",
      "Epoch 20 complete, total errors is 26.400673271838674\n",
      "Epoch 21 complete, total errors is 26.4672674807646\n",
      "Epoch 22 complete, total errors is 26.31279074463818\n",
      "Epoch 23 complete, total errors is 26.403235593322147\n",
      "Epoch 24 complete, total errors is 26.37929408396605\n",
      "Epoch 25 complete, total errors is 26.34850609602097\n",
      "Epoch 26 complete, total errors is 26.393387178012883\n",
      "Epoch 27 complete, total errors is 26.42682296193343\n",
      "Epoch 28 complete, total errors is 26.376606707731746\n",
      "Epoch 29 complete, total errors is 26.516590301193112\n",
      "Epoch 30 complete, total errors is 26.46740919618746\n",
      "Epoch 31 complete, total errors is 26.322400377905673\n",
      "Epoch 32 complete, total errors is 26.42466128943545\n",
      "Epoch 33 complete, total errors is 26.315243609358042\n",
      "Epoch 34 complete, total errors is 26.41196464365786\n",
      "Epoch 35 complete, total errors is 26.49834885080941\n",
      "Epoch 36 complete, total errors is 26.361659613446104\n",
      "Epoch 37 complete, total errors is 26.387985551156955\n",
      "Epoch 38 complete, total errors is 26.323365561981436\n",
      "Epoch 39 complete, total errors is 26.469630756577477\n",
      "Epoch 40 complete, total errors is 26.340550981507928\n",
      "Epoch 41 complete, total errors is 26.335707410673102\n",
      "Epoch 42 complete, total errors is 26.356948286008162\n",
      "Epoch 43 complete, total errors is 26.348061609098618\n",
      "Epoch 44 complete, total errors is 26.39605251834128\n",
      "Epoch 45 complete, total errors is 26.436128002359958\n",
      "Epoch 46 complete, total errors is 26.335670521164484\n",
      "Epoch 47 complete, total errors is 26.3324242151248\n",
      "Epoch 48 complete, total errors is 26.303997823289862\n",
      "Epoch 49 complete, total errors is 26.306647704690462\n",
      "Epoch 50 complete, total errors is 26.342255249127387\n",
      "Epoch 51 complete, total errors is 26.336428227418416\n",
      "Epoch 52 complete, total errors is 26.306081473395842\n",
      "Epoch 53 complete, total errors is 26.302893864442474\n",
      "Epoch 54 complete, total errors is 26.30470690421214\n",
      "Epoch 55 complete, total errors is 26.317965559426824\n",
      "Epoch 56 complete, total errors is 26.30472778136084\n",
      "Epoch 57 complete, total errors is 26.315495540839564\n",
      "Epoch 58 complete, total errors is 26.31076774749799\n",
      "Epoch 59 complete, total errors is 26.303474406550492\n",
      "Epoch 60 complete, total errors is 26.323565751339487\n",
      "Epoch 61 complete, total errors is 26.303391176533808\n",
      "Epoch 62 complete, total errors is 26.326309904102807\n",
      "Epoch 63 complete, total errors is 26.304974655965353\n",
      "Epoch 64 complete, total errors is 26.304641040268045\n",
      "Epoch 65 complete, total errors is 26.311257782074154\n",
      "Epoch 66 complete, total errors is 26.302994886869847\n",
      "Epoch 67 complete, total errors is 26.30308940818407\n",
      "Epoch 68 complete, total errors is 26.307882719225113\n",
      "Epoch 69 complete, total errors is 26.304449506823044\n",
      "Epoch 70 complete, total errors is 26.315772831977473\n",
      "Epoch 71 complete, total errors is 26.303145401959476\n",
      "Epoch 72 complete, total errors is 26.304308605453727\n",
      "Epoch 73 complete, total errors is 26.3190891855214\n",
      "Epoch 74 complete, total errors is 26.312439489768217\n",
      "Epoch 75 complete, total errors is 26.308594456377193\n",
      "Epoch 76 complete, total errors is 26.307019007518583\n",
      "Epoch 77 complete, total errors is 26.30320334389603\n",
      "Epoch 78 complete, total errors is 26.302789165473236\n",
      "Epoch 79 complete, total errors is 26.32877419531217\n",
      "Epoch 80 complete, total errors is 26.308344526196503\n",
      "Epoch 81 complete, total errors is 26.307475405376174\n",
      "Epoch 82 complete, total errors is 26.302733285548896\n",
      "Epoch 83 complete, total errors is 26.306047160305045\n",
      "Epoch 84 complete, total errors is 26.304378872156697\n",
      "Epoch 85 complete, total errors is 26.346039825235497\n",
      "Epoch 86 complete, total errors is 26.30339018516944\n",
      "Epoch 87 complete, total errors is 26.304300682889547\n",
      "Epoch 88 complete, total errors is 26.303453915586164\n",
      "Epoch 89 complete, total errors is 26.30494323228406\n",
      "Epoch 90 complete, total errors is 26.30372638829885\n",
      "Epoch 91 complete, total errors is 26.303701835617026\n",
      "Epoch 92 complete, total errors is 26.305776415639713\n",
      "Epoch 93 complete, total errors is 26.302702223111037\n",
      "Epoch 94 complete, total errors is 26.303237287372333\n",
      "Epoch 95 complete, total errors is 26.308967899977837\n",
      "Epoch 96 complete, total errors is 26.31603513587671\n",
      "Epoch 97 complete, total errors is 26.303233750864486\n",
      "Epoch 98 complete, total errors is 26.307265674742794\n",
      "Epoch 99 complete, total errors is 26.31329385197745\n",
      "Epoch 100 complete, total errors is 26.304782592329836\n",
      "Epoch 101 complete, total errors is 26.303290210966207\n",
      "Epoch 102 complete, total errors is 26.302752987987233\n",
      "Epoch 103 complete, total errors is 26.343594423529257\n",
      "Epoch 104 complete, total errors is 26.307013250933814\n",
      "Epoch 105 complete, total errors is 26.304862427885134\n",
      "Epoch 106 complete, total errors is 26.314623734807448\n",
      "Epoch 107 complete, total errors is 26.302699681225736\n",
      "Epoch 108 complete, total errors is 26.30308164681693\n",
      "Epoch 109 complete, total errors is 26.30468025734516\n",
      "Epoch 110 complete, total errors is 26.30710380179559\n",
      "Epoch 111 complete, total errors is 26.30966330726484\n",
      "Epoch 112 complete, total errors is 26.311289138034667\n",
      "Epoch 113 complete, total errors is 26.30828875864796\n",
      "Epoch 114 complete, total errors is 26.303953277978344\n",
      "Epoch 115 complete, total errors is 26.304317627500645\n",
      "Epoch 116 complete, total errors is 26.310373550768983\n",
      "Epoch 117 complete, total errors is 26.304794203086857\n",
      "Epoch 118 complete, total errors is 26.30415036485582\n",
      "Epoch 119 complete, total errors is 26.302703454205105\n",
      "Epoch 120 complete, total errors is 26.305149111889623\n",
      "Epoch 121 complete, total errors is 26.313825000982426\n",
      "Epoch 122 complete, total errors is 26.302918545057288\n",
      "Epoch 123 complete, total errors is 26.30759074332201\n",
      "Epoch 124 complete, total errors is 26.318091043747025\n",
      "Epoch 125 complete, total errors is 26.313017493139732\n",
      "Epoch 126 complete, total errors is 26.306619624450043\n",
      "Epoch 127 complete, total errors is 26.302913401271837\n",
      "Epoch 128 complete, total errors is 26.318248938599673\n",
      "Epoch 129 complete, total errors is 26.306282684452206\n",
      "Epoch 130 complete, total errors is 26.359818581117654\n",
      "Epoch 131 complete, total errors is 26.307393290146067\n",
      "Epoch 132 complete, total errors is 26.302702087214627\n",
      "Epoch 133 complete, total errors is 26.302796654105816\n",
      "Epoch 134 complete, total errors is 26.310929156850793\n",
      "Epoch 135 complete, total errors is 26.313461393407337\n",
      "Epoch 136 complete, total errors is 26.302812933978352\n",
      "Epoch 137 complete, total errors is 26.309004079067435\n",
      "Epoch 138 complete, total errors is 26.30455716267107\n",
      "Epoch 139 complete, total errors is 26.303504840148157\n",
      "Epoch 140 complete, total errors is 26.331610462019068\n",
      "Epoch 141 complete, total errors is 26.304653733453506\n",
      "Epoch 142 complete, total errors is 26.309924244264643\n",
      "Epoch 143 complete, total errors is 26.30953779885968\n",
      "Epoch 144 complete, total errors is 26.303900038288823\n",
      "Epoch 145 complete, total errors is 26.30274136438593\n",
      "Epoch 146 complete, total errors is 26.30293277197608\n",
      "Epoch 147 complete, total errors is 26.31075716814712\n",
      "Epoch 148 complete, total errors is 26.336265241699174\n",
      "Epoch 149 complete, total errors is 26.302907399051517\n",
      "Epoch 150 complete, total errors is 26.305471580671913\n",
      "Epoch 151 complete, total errors is 26.302712994762494\n",
      "Epoch 152 complete, total errors is 26.31757058011935\n",
      "Epoch 153 complete, total errors is 26.304492257284892\n",
      "Epoch 154 complete, total errors is 26.330695598808916\n",
      "Epoch 155 complete, total errors is 26.304049885264767\n",
      "Epoch 156 complete, total errors is 26.303876955497685\n",
      "Epoch 157 complete, total errors is 26.30342114569593\n",
      "Epoch 158 complete, total errors is 26.30618715579859\n",
      "Epoch 159 complete, total errors is 26.305008188352307\n",
      "Epoch 160 complete, total errors is 26.304950432173882\n",
      "Epoch 161 complete, total errors is 26.317011719185487\n",
      "Epoch 162 complete, total errors is 26.304946116563272\n",
      "Epoch 163 complete, total errors is 26.302701383698455\n",
      "Epoch 164 complete, total errors is 26.316762151783028\n",
      "Epoch 165 complete, total errors is 26.307139694269203\n",
      "Epoch 166 complete, total errors is 26.32154291539409\n",
      "Epoch 167 complete, total errors is 26.306183117266258\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 168 complete, total errors is 26.303571159506106\n",
      "Epoch 169 complete, total errors is 26.315621411135517\n",
      "Epoch 170 complete, total errors is 26.315365085468663\n",
      "Epoch 171 complete, total errors is 26.329720183012075\n",
      "Epoch 172 complete, total errors is 26.304973964891857\n",
      "Epoch 173 complete, total errors is 26.30380455941927\n",
      "Epoch 174 complete, total errors is 26.30689593670007\n",
      "Epoch 175 complete, total errors is 26.304155297493146\n",
      "Epoch 176 complete, total errors is 26.310186757018563\n",
      "Epoch 177 complete, total errors is 26.3047500098045\n",
      "Epoch 178 complete, total errors is 26.30312217931051\n",
      "Epoch 179 complete, total errors is 26.321343344123818\n",
      "Epoch 180 complete, total errors is 26.307160609948426\n",
      "Epoch 181 complete, total errors is 26.311836718859702\n",
      "Epoch 182 complete, total errors is 26.308586009313693\n",
      "Epoch 183 complete, total errors is 26.315925722123573\n",
      "Epoch 184 complete, total errors is 26.304415558925676\n",
      "Epoch 185 complete, total errors is 26.31904246955906\n",
      "Epoch 186 complete, total errors is 26.303092615411025\n",
      "Epoch 187 complete, total errors is 26.312948161025012\n",
      "Epoch 188 complete, total errors is 26.30563634091719\n",
      "Epoch 189 complete, total errors is 26.307925142691488\n",
      "Epoch 190 complete, total errors is 26.311287731628937\n",
      "Epoch 191 complete, total errors is 26.30359526804959\n",
      "Epoch 192 complete, total errors is 26.30271470540086\n",
      "Epoch 193 complete, total errors is 26.305730923015847\n",
      "Epoch 194 complete, total errors is 26.328751154211815\n",
      "Epoch 195 complete, total errors is 26.304532529928913\n",
      "Epoch 196 complete, total errors is 26.302878763558812\n",
      "Epoch 197 complete, total errors is 26.331344805067925\n",
      "Epoch 198 complete, total errors is 26.30307411026535\n",
      "Epoch 199 complete, total errors is 26.31432869419953\n",
      "Epoch 200 complete, total errors is 26.306323794829535\n",
      "Epoch 201 complete, total errors is 26.303877047264784\n",
      "Epoch 202 complete, total errors is 26.3036824147959\n",
      "Epoch 203 complete, total errors is 26.31398574813143\n",
      "Epoch 204 complete, total errors is 26.303766876811817\n",
      "Epoch 205 complete, total errors is 26.308632334666477\n",
      "Epoch 206 complete, total errors is 26.306928535667694\n",
      "Epoch 207 complete, total errors is 26.302930848269497\n",
      "Epoch 208 complete, total errors is 26.306616594862646\n",
      "Epoch 209 complete, total errors is 26.304419470741067\n",
      "Epoch 210 complete, total errors is 26.31041189611147\n",
      "Epoch 211 complete, total errors is 26.305869603875017\n",
      "Epoch 212 complete, total errors is 26.302731103108727\n",
      "Epoch 213 complete, total errors is 26.304596408233316\n",
      "Epoch 214 complete, total errors is 26.302741564689683\n",
      "Epoch 215 complete, total errors is 26.302756444426695\n",
      "Epoch 216 complete, total errors is 26.30338954115882\n",
      "Epoch 217 complete, total errors is 26.309958714843386\n",
      "Epoch 218 complete, total errors is 26.318146720666252\n",
      "Epoch 219 complete, total errors is 26.305248690030666\n",
      "Epoch 220 complete, total errors is 26.302830034252764\n",
      "Epoch 221 complete, total errors is 26.311747215745168\n",
      "Epoch 222 complete, total errors is 26.30755573269188\n",
      "Epoch 223 complete, total errors is 26.306746438060962\n",
      "Epoch 224 complete, total errors is 26.305098314140565\n",
      "Epoch 225 complete, total errors is 26.318885135410977\n",
      "Epoch 226 complete, total errors is 26.318749261591343\n",
      "Epoch 227 complete, total errors is 26.321944546838708\n",
      "Epoch 228 complete, total errors is 26.302700529886426\n",
      "Epoch 229 complete, total errors is 26.308458573577596\n",
      "Epoch 230 complete, total errors is 26.3037953055117\n",
      "Epoch 231 complete, total errors is 26.31053436717997\n",
      "Epoch 232 complete, total errors is 26.315047397769643\n",
      "Epoch 233 complete, total errors is 26.308057842931404\n",
      "Epoch 234 complete, total errors is 26.313131724780696\n",
      "Epoch 235 complete, total errors is 26.316958473238046\n",
      "Epoch 236 complete, total errors is 26.312156518292323\n",
      "Epoch 237 complete, total errors is 26.314300378240482\n",
      "Epoch 238 complete, total errors is 26.306510889123576\n",
      "Epoch 239 complete, total errors is 26.303283961579847\n",
      "Epoch 240 complete, total errors is 26.304335677318917\n",
      "Epoch 241 complete, total errors is 26.313272266539705\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "Epoch 331 complete, total errors is 26.30568098305675\n",
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     ]
    },
    {
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     "output_type": "stream",
     "text": [
      "Epoch 503 complete, total errors is 26.421951062454482\n",
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      "Epoch 586 complete, total errors is 26.455519764459645\n",
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      "Epoch 655 complete, total errors is 26.345276576749917\n",
      "Epoch 656 complete, total errors is 26.825587412752387\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 657 complete, total errors is 26.33696912143624\n",
      "Epoch 658 complete, total errors is 27.06944584390837\n",
      "Epoch 659 complete, total errors is 26.67609675424614\n",
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      "Epoch 710 complete, total errors is 35.491322384284715\n",
      "Epoch 711 complete, total errors is 26.887819234557764\n",
      "Epoch 712 complete, total errors is 26.641750549853633\n",
      "Epoch 713 complete, total errors is 26.84554480364122\n",
      "Epoch 714 complete, total errors is 26.9181931944934\n",
      "Epoch 715 complete, total errors is 26.835497082235207\n",
      "Epoch 716 complete, total errors is 26.81710973875814\n",
      "Epoch 717 complete, total errors is 26.94758967251917\n",
      "Epoch 718 complete, total errors is 27.004032729157835\n",
      "Epoch 719 complete, total errors is 26.85478693084546\n",
      "Epoch 720 complete, total errors is 26.562883697886008\n",
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      "Epoch 727 complete, total errors is 26.326169625552073\n",
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      "Epoch 831 complete, total errors is 27.234695410774094\n",
      "Epoch 832 complete, total errors is 26.93146998516569\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 833 complete, total errors is 26.965162209449296\n",
      "Epoch 834 complete, total errors is 27.229799128742854\n",
      "Epoch 835 complete, total errors is 26.321879106967437\n",
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      "Epoch 841 complete, total errors is 30.922796064132648\n",
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      "Epoch 850 complete, total errors is 26.919345558280813\n",
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      "Epoch 870 complete, total errors is 43.07371678964381\n",
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      "Epoch 888 complete, total errors is 27.1688821537442\n",
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      "Epoch 900 complete, total errors is 27.181682532644842\n",
      "Epoch 901 complete, total errors is 32.19213121831385\n",
      "Epoch 902 complete, total errors is 27.15267079221044\n",
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      "Epoch 907 complete, total errors is 43.71353177973119\n",
      "Epoch 908 complete, total errors is 26.996281297708997\n",
      "Epoch 909 complete, total errors is 26.897673966333493\n",
      "Epoch 910 complete, total errors is 27.25116983112779\n",
      "Epoch 911 complete, total errors is 27.175896591734613\n",
      "Epoch 912 complete, total errors is 26.437182614176614\n",
      "Epoch 913 complete, total errors is 27.257587609098042\n",
      "Epoch 914 complete, total errors is 26.869375537613067\n",
      "Epoch 915 complete, total errors is 26.406798223262605\n",
      "Epoch 916 complete, total errors is 27.17199596531034\n",
      "Epoch 917 complete, total errors is 30.159627372662527\n",
      "Epoch 918 complete, total errors is 27.399402519653833\n",
      "Epoch 919 complete, total errors is 27.128772538470287\n",
      "Epoch 920 complete, total errors is 27.168267695030593\n",
      "Epoch 921 complete, total errors is 27.023030638478374\n",
      "Epoch 922 complete, total errors is 27.21568229564459\n",
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      "Epoch 994 complete, total errors is 27.305108136667364\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 995 complete, total errors is 27.147219452341865\n",
      "Epoch 996 complete, total errors is 27.388213256148035\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1158 complete, total errors is 27.3524219656647\n",
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      "Epoch 1254 complete, total errors is 28.515945918287777\n",
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      "Epoch 1256 complete, total errors is 42.41022229382024\n",
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      "Epoch 1333 complete, total errors is 27.471726365177805\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1334 complete, total errors is 27.527675474311117\n",
      "Epoch 1335 complete, total errors is 27.33934705084109\n",
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      "Epoch 1490 complete, total errors is 27.289987230166115\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1491 complete, total errors is 27.672590726695596\n",
      "Epoch 1492 complete, total errors is 49.86946193367255\n",
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      "Epoch 1586 complete, total errors is 42.61482758073771\n",
      "Epoch 1587 complete, total errors is 27.63934494184905\n",
      "Epoch 1588 complete, total errors is 27.26328624928079\n",
      "Epoch 1589 complete, total errors is 27.375547700473877\n",
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      "Epoch 1591 complete, total errors is 39.69362083564616\n",
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      "Epoch 1593 complete, total errors is 26.41673792450074\n",
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      "Epoch 1597 complete, total errors is 26.302721734726642\n",
      "Epoch 1598 complete, total errors is 27.485616044682242\n",
      "Epoch 1599 complete, total errors is 27.32261978518318\n",
      "Epoch 1600 complete, total errors is 42.65339925337759\n",
      "Epoch 1601 complete, total errors is 27.6317128655516\n",
      "Epoch 1602 complete, total errors is 27.474820745323832\n",
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      "Epoch 1609 complete, total errors is 27.49148891826242\n",
      "Epoch 1610 complete, total errors is 55.61502118471054\n",
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      "Epoch 1613 complete, total errors is 27.67565228200715\n",
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      "Epoch 1616 complete, total errors is 27.71167194475464\n",
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      "Epoch 1619 complete, total errors is 36.88951425652095\n",
      "Epoch 1620 complete, total errors is 26.45288573243164\n",
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      "Epoch 1624 complete, total errors is 27.457465998311868\n",
      "Epoch 1625 complete, total errors is 27.19558800127728\n",
      "Epoch 1626 complete, total errors is 27.442432699114875\n",
      "Epoch 1627 complete, total errors is 30.0084198755278\n",
      "Epoch 1628 complete, total errors is 27.370041835946488\n",
      "Epoch 1629 complete, total errors is 27.61764153070058\n",
      "Epoch 1630 complete, total errors is 53.335625105004276\n",
      "Epoch 1631 complete, total errors is 47.030548322443536\n",
      "Epoch 1632 complete, total errors is 27.45159283155027\n",
      "Epoch 1633 complete, total errors is 27.536249619588148\n",
      "Epoch 1634 complete, total errors is 27.337332793579467\n",
      "Epoch 1635 complete, total errors is 27.516813282802197\n",
      "Epoch 1636 complete, total errors is 32.13030478905456\n",
      "Epoch 1637 complete, total errors is 27.343115412961104\n",
      "Epoch 1638 complete, total errors is 27.388027152622534\n",
      "Epoch 1639 complete, total errors is 27.59082458107902\n",
      "Epoch 1640 complete, total errors is 27.240201445357812\n",
      "Epoch 1641 complete, total errors is 27.470164775171312\n",
      "Epoch 1642 complete, total errors is 27.199959462560464\n",
      "Epoch 1643 complete, total errors is 30.03109822304664\n",
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      "Epoch 1645 complete, total errors is 27.33933218085488\n",
      "Epoch 1646 complete, total errors is 27.433119931003475\n",
      "Epoch 1647 complete, total errors is 27.412900080544794\n",
      "Epoch 1648 complete, total errors is 28.7698113221062\n",
      "Epoch 1649 complete, total errors is 27.5703724903115\n",
      "Epoch 1650 complete, total errors is 27.358707483395985\n",
      "Epoch 1651 complete, total errors is 26.50154539242087\n",
      "Epoch 1652 complete, total errors is 27.05172492787765\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1653 complete, total errors is 26.658431811352315\n",
      "Epoch 1654 complete, total errors is 27.461028476499685\n",
      "Epoch 1655 complete, total errors is 27.333074606345672\n",
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      "Epoch 1700 complete, total errors is 42.42966744672289\n",
      "Epoch 1701 complete, total errors is 26.851391655031954\n",
      "Epoch 1702 complete, total errors is 37.34920590845227\n",
      "Epoch 1703 complete, total errors is 27.374273284871723\n",
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      "Epoch 1707 complete, total errors is 26.321714530899428\n",
      "Epoch 1708 complete, total errors is 27.467893483757887\n",
      "Epoch 1709 complete, total errors is 27.539708332780158\n",
      "Epoch 1710 complete, total errors is 26.45966155743173\n",
      "Epoch 1711 complete, total errors is 27.31659062771777\n",
      "Epoch 1712 complete, total errors is 27.467029263784053\n",
      "Epoch 1713 complete, total errors is 51.35335449965496\n",
      "Epoch 1714 complete, total errors is 30.209819432922238\n",
      "Epoch 1715 complete, total errors is 39.74244972047265\n",
      "Epoch 1716 complete, total errors is 27.440131035265303\n",
      "Epoch 1717 complete, total errors is 27.350183261319998\n",
      "Epoch 1718 complete, total errors is 27.71505321216434\n",
      "Epoch 1719 complete, total errors is 27.61706672973051\n",
      "Epoch 1720 complete, total errors is 27.666829733600625\n",
      "Epoch 1721 complete, total errors is 27.027046129805406\n",
      "Epoch 1722 complete, total errors is 27.548054841853887\n",
      "Epoch 1723 complete, total errors is 27.529845330571476\n",
      "Epoch 1724 complete, total errors is 26.37431092722386\n",
      "Epoch 1725 complete, total errors is 56.21332713416349\n",
      "Epoch 1726 complete, total errors is 27.534419705645025\n",
      "Epoch 1727 complete, total errors is 27.386612422130842\n",
      "Epoch 1728 complete, total errors is 27.67298582353536\n",
      "Epoch 1729 complete, total errors is 27.501928276064252\n",
      "Epoch 1730 complete, total errors is 27.56372938845038\n",
      "Epoch 1731 complete, total errors is 26.900747214017382\n",
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      "Epoch 1733 complete, total errors is 28.579338598149153\n",
      "Epoch 1734 complete, total errors is 27.33996833884917\n",
      "Epoch 1735 complete, total errors is 27.209147160816023\n",
      "Epoch 1736 complete, total errors is 27.531872332058043\n",
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      "Epoch 1738 complete, total errors is 27.569030212408514\n",
      "Epoch 1739 complete, total errors is 27.351537583570288\n",
      "Epoch 1740 complete, total errors is 27.541634096326757\n",
      "Epoch 1741 complete, total errors is 27.245726426944266\n",
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      "Epoch 1759 complete, total errors is 52.96805016722105\n",
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      "Epoch 1765 complete, total errors is 27.207423661190333\n",
      "Epoch 1766 complete, total errors is 27.308783360615763\n",
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      "Epoch 1768 complete, total errors is 56.47775313966145\n",
      "Epoch 1769 complete, total errors is 27.479473081779823\n",
      "Epoch 1770 complete, total errors is 37.185474963989975\n",
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      "Epoch 1806 complete, total errors is 28.46228402266138\n",
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      "Epoch 1808 complete, total errors is 27.389675541801424\n",
      "Epoch 1809 complete, total errors is 27.476148341039632\n",
      "Epoch 1810 complete, total errors is 27.409272776293733\n",
      "Epoch 1811 complete, total errors is 27.386091410966056\n",
      "Epoch 1812 complete, total errors is 27.49642082109167\n",
      "Epoch 1813 complete, total errors is 27.31054121506342\n",
      "Epoch 1814 complete, total errors is 27.63737827168444\n",
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      "Epoch 1816 complete, total errors is 56.54539751529364\n",
      "Epoch 1817 complete, total errors is 52.124846861758016\n",
      "Epoch 1818 complete, total errors is 56.65337266325041\n",
      "Epoch 1819 complete, total errors is 27.441358695337613\n",
      "Epoch 1820 complete, total errors is 27.490995484194098\n",
      "Epoch 1821 complete, total errors is 52.25414394807251\n",
      "Epoch 1822 complete, total errors is 56.15562593690642\n",
      "Epoch 1823 complete, total errors is 27.306802363933652\n",
      "Epoch 1824 complete, total errors is 27.609917816098648\n",
      "Epoch 1825 complete, total errors is 27.389045127328167\n",
      "Epoch 1826 complete, total errors is 27.117865981275145\n",
      "Epoch 1827 complete, total errors is 27.557177375887914\n",
      "Epoch 1828 complete, total errors is 27.464794585741174\n",
      "Epoch 1829 complete, total errors is 27.343931567288166\n",
      "Epoch 1830 complete, total errors is 27.51852467825948\n",
      "Epoch 1831 complete, total errors is 27.435713136278512\n",
      "Epoch 1832 complete, total errors is 27.301285937499536\n",
      "Epoch 1833 complete, total errors is 37.42255073603644\n",
      "Epoch 1834 complete, total errors is 26.725235500749307\n",
      "Epoch 1835 complete, total errors is 27.45770387465842\n",
      "Epoch 1836 complete, total errors is 27.478407793715284\n",
      "Epoch 1837 complete, total errors is 27.073852137732654\n",
      "Epoch 1838 complete, total errors is 27.411816466022373\n",
      "Epoch 1839 complete, total errors is 27.406406924776842\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1840 complete, total errors is 27.803367092547134\n",
      "Epoch 1841 complete, total errors is 37.48570190909856\n",
      "Epoch 1842 complete, total errors is 27.543906366538504\n",
      "Epoch 1843 complete, total errors is 27.663372820025927\n",
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      "Epoch 1845 complete, total errors is 27.14188359708291\n",
      "Epoch 1846 complete, total errors is 27.55383991457412\n",
      "Epoch 1847 complete, total errors is 27.567131448032665\n",
      "Epoch 1848 complete, total errors is 27.598630683029853\n",
      "Epoch 1849 complete, total errors is 27.197502061136113\n",
      "Epoch 1850 complete, total errors is 27.625012624112014\n",
      "Epoch 1851 complete, total errors is 27.813252300081032\n",
      "Epoch 1852 complete, total errors is 27.2340009385087\n",
      "Epoch 1853 complete, total errors is 27.293145480863448\n",
      "Epoch 1854 complete, total errors is 27.354711584465228\n",
      "Epoch 1855 complete, total errors is 27.53074860050081\n",
      "Epoch 1856 complete, total errors is 56.463210565870696\n",
      "Epoch 1857 complete, total errors is 27.381498288041122\n",
      "Epoch 1858 complete, total errors is 27.273383186875925\n",
      "Epoch 1859 complete, total errors is 27.33107152759203\n",
      "Epoch 1860 complete, total errors is 27.791415295696563\n",
      "Epoch 1861 complete, total errors is 27.49063475993446\n",
      "Epoch 1862 complete, total errors is 27.511047546632078\n",
      "Epoch 1863 complete, total errors is 26.82822305796923\n",
      "Epoch 1864 complete, total errors is 27.524848227870855\n",
      "Epoch 1865 complete, total errors is 27.65110480325875\n",
      "Epoch 1866 complete, total errors is 27.43883601531634\n",
      "Epoch 1867 complete, total errors is 51.26991701631403\n",
      "Epoch 1868 complete, total errors is 27.45719560158627\n",
      "Epoch 1869 complete, total errors is 27.391650317236582\n",
      "Epoch 1870 complete, total errors is 27.33076222954755\n",
      "Epoch 1871 complete, total errors is 27.561089601241342\n",
      "Epoch 1872 complete, total errors is 27.503843710275614\n",
      "Epoch 1873 complete, total errors is 30.566325211802436\n",
      "Epoch 1874 complete, total errors is 26.57685425516449\n",
      "Epoch 1875 complete, total errors is 27.63874610917065\n",
      "Epoch 1876 complete, total errors is 40.53436237360197\n",
      "Epoch 1877 complete, total errors is 27.39672877511486\n",
      "Epoch 1878 complete, total errors is 27.739239393614127\n",
      "Epoch 1879 complete, total errors is 27.10171275001488\n",
      "Epoch 1880 complete, total errors is 27.489941802800857\n",
      "Epoch 1881 complete, total errors is 26.695405688223126\n",
      "Epoch 1882 complete, total errors is 27.343847495639057\n",
      "Epoch 1883 complete, total errors is 27.547379749630963\n",
      "Epoch 1884 complete, total errors is 27.505801001282634\n",
      "Epoch 1885 complete, total errors is 27.57457552287137\n",
      "Epoch 1886 complete, total errors is 27.337791803147013\n",
      "Epoch 1887 complete, total errors is 57.231480390684595\n",
      "Epoch 1888 complete, total errors is 26.960386701847707\n",
      "Epoch 1889 complete, total errors is 27.518521794678442\n",
      "Epoch 1890 complete, total errors is 27.327772076669067\n",
      "Epoch 1891 complete, total errors is 27.454099255031903\n",
      "Epoch 1892 complete, total errors is 27.38749705666512\n",
      "Epoch 1893 complete, total errors is 27.48126853101378\n",
      "Epoch 1894 complete, total errors is 27.368841652989076\n",
      "Epoch 1895 complete, total errors is 27.27101392832718\n",
      "Epoch 1896 complete, total errors is 27.685596153598382\n",
      "Epoch 1897 complete, total errors is 35.07119403855028\n",
      "Epoch 1898 complete, total errors is 27.591913070162803\n",
      "Epoch 1899 complete, total errors is 26.371911127335437\n",
      "Epoch 1900 complete, total errors is 52.61879903217341\n",
      "Epoch 1901 complete, total errors is 27.36985729286379\n",
      "Epoch 1902 complete, total errors is 26.308961959552764\n",
      "Epoch 1903 complete, total errors is 27.490465786988004\n",
      "Epoch 1904 complete, total errors is 27.527003987144994\n",
      "Epoch 1905 complete, total errors is 27.388770465979043\n",
      "Epoch 1906 complete, total errors is 27.37071632881154\n",
      "Epoch 1907 complete, total errors is 56.31718180693093\n",
      "Epoch 1908 complete, total errors is 27.39178515776603\n",
      "Epoch 1909 complete, total errors is 27.609997198264054\n",
      "Epoch 1910 complete, total errors is 27.430202477578376\n",
      "Epoch 1911 complete, total errors is 26.983205865005566\n",
      "Epoch 1912 complete, total errors is 27.40408187048472\n",
      "Epoch 1913 complete, total errors is 27.39293954950182\n",
      "Epoch 1914 complete, total errors is 27.43250595874082\n",
      "Epoch 1915 complete, total errors is 27.074089276825433\n",
      "Epoch 1916 complete, total errors is 27.72087852954143\n",
      "Epoch 1917 complete, total errors is 27.652196858875683\n",
      "Epoch 1918 complete, total errors is 27.078556233072625\n",
      "Epoch 1919 complete, total errors is 27.319309100318634\n",
      "Epoch 1920 complete, total errors is 27.305989873263115\n",
      "Epoch 1921 complete, total errors is 27.442034244454163\n",
      "Epoch 1922 complete, total errors is 27.426425045113845\n",
      "Epoch 1923 complete, total errors is 35.230299162104764\n",
      "Epoch 1924 complete, total errors is 27.1444414123769\n",
      "Epoch 1925 complete, total errors is 27.57867536749156\n",
      "Epoch 1926 complete, total errors is 27.43000014790244\n",
      "Epoch 1927 complete, total errors is 26.925590134060194\n",
      "Epoch 1928 complete, total errors is 27.564622352360008\n",
      "Epoch 1929 complete, total errors is 27.344510367492056\n",
      "Epoch 1930 complete, total errors is 27.370004526104164\n",
      "Epoch 1931 complete, total errors is 27.32482403185842\n",
      "Epoch 1932 complete, total errors is 27.514462264792876\n",
      "Epoch 1933 complete, total errors is 27.435091318403842\n",
      "Epoch 1934 complete, total errors is 27.50258275187652\n",
      "Epoch 1935 complete, total errors is 27.501913437603704\n",
      "Epoch 1936 complete, total errors is 27.34334515792117\n",
      "Epoch 1937 complete, total errors is 27.17995005102538\n",
      "Epoch 1938 complete, total errors is 27.431888399528965\n",
      "Epoch 1939 complete, total errors is 27.424789051044378\n",
      "Epoch 1940 complete, total errors is 27.567413790262563\n",
      "Epoch 1941 complete, total errors is 27.38392145195809\n",
      "Epoch 1942 complete, total errors is 26.902963185206367\n",
      "Epoch 1943 complete, total errors is 27.64416237559966\n",
      "Epoch 1944 complete, total errors is 51.40142912811878\n",
      "Epoch 1945 complete, total errors is 26.314870021156317\n",
      "Epoch 1946 complete, total errors is 27.553263812347808\n",
      "Epoch 1947 complete, total errors is 27.444585563215\n",
      "Epoch 1948 complete, total errors is 27.390666578670217\n",
      "Epoch 1949 complete, total errors is 27.464733275260613\n",
      "Epoch 1950 complete, total errors is 27.304911075673438\n",
      "Epoch 1951 complete, total errors is 27.417737808615268\n",
      "Epoch 1952 complete, total errors is 56.96659124219629\n",
      "Epoch 1953 complete, total errors is 27.61946150718052\n",
      "Epoch 1954 complete, total errors is 27.41814449177191\n",
      "Epoch 1955 complete, total errors is 27.428047552565587\n",
      "Epoch 1956 complete, total errors is 27.662269637387098\n",
      "Epoch 1957 complete, total errors is 52.77022104601147\n",
      "Epoch 1958 complete, total errors is 56.757494468456116\n",
      "Epoch 1959 complete, total errors is 26.71533202670784\n",
      "Epoch 1960 complete, total errors is 54.35461280217053\n",
      "Epoch 1961 complete, total errors is 54.38785806222565\n",
      "Epoch 1962 complete, total errors is 56.47459862939043\n",
      "Epoch 1963 complete, total errors is 56.9973787026213\n",
      "Epoch 1964 complete, total errors is 27.45962797264584\n",
      "Epoch 1965 complete, total errors is 27.499957386948907\n",
      "Epoch 1966 complete, total errors is 30.293252141715087\n",
      "Epoch 1967 complete, total errors is 27.56595917647457\n",
      "Epoch 1968 complete, total errors is 27.501047964241998\n",
      "Epoch 1969 complete, total errors is 57.23588141045807\n",
      "Epoch 1970 complete, total errors is 27.470024938079238\n",
      "Epoch 1971 complete, total errors is 49.53086606825525\n",
      "Epoch 1972 complete, total errors is 43.851536676929406\n",
      "Epoch 1973 complete, total errors is 27.605869432814004\n",
      "Epoch 1974 complete, total errors is 27.509684589904285\n",
      "Epoch 1975 complete, total errors is 27.02006966867814\n",
      "Epoch 1976 complete, total errors is 51.82493869508579\n",
      "Epoch 1977 complete, total errors is 52.76210266337132\n",
      "Epoch 1978 complete, total errors is 27.188716949561563\n",
      "Epoch 1979 complete, total errors is 27.282863469577155\n",
      "Epoch 1980 complete, total errors is 27.524368790982102\n",
      "Epoch 1981 complete, total errors is 27.439184938749527\n",
      "Epoch 1982 complete, total errors is 27.442676480733354\n",
      "Epoch 1983 complete, total errors is 27.54321615374125\n",
      "Epoch 1984 complete, total errors is 27.39667953089907\n",
      "Epoch 1985 complete, total errors is 54.70795955829958\n",
      "Epoch 1986 complete, total errors is 27.271817768825926\n",
      "Epoch 1987 complete, total errors is 27.402970929857368\n",
      "Epoch 1988 complete, total errors is 27.32275415069541\n",
      "Epoch 1989 complete, total errors is 27.378423147590617\n",
      "Epoch 1990 complete, total errors is 27.441334516335733\n",
      "Epoch 1991 complete, total errors is 27.609503389093454\n",
      "Epoch 1992 complete, total errors is 41.31262662917108\n",
      "Epoch 1993 complete, total errors is 27.40115195767368\n",
      "Epoch 1994 complete, total errors is 51.5357382230446\n",
      "Epoch 1995 complete, total errors is 27.44968324837525\n",
      "Epoch 1996 complete, total errors is 27.504745410305084\n",
      "Epoch 1997 complete, total errors is 26.807010814912807\n",
      "Epoch 1998 complete, total errors is 27.587067610412554\n",
      "Epoch 1999 complete, total errors is 27.36060141322738\n",
      "Epoch 2000 complete, total errors is 27.34390001228121\n",
      "Epoch 2001 complete, total errors is 27.62759157444995\n",
      "Epoch 2002 complete, total errors is 55.04623665579716\n",
      "Epoch 2003 complete, total errors is 27.414209909004228\n",
      "Epoch 2004 complete, total errors is 27.30506597851663\n",
      "Epoch 2005 complete, total errors is 27.43175054998011\n",
      "Epoch 2006 complete, total errors is 28.639008418395626\n",
      "Epoch 2007 complete, total errors is 27.336538360489264\n",
      "Epoch 2008 complete, total errors is 27.44240067573729\n",
      "Epoch 2009 complete, total errors is 27.627670569340154\n",
      "Epoch 2010 complete, total errors is 27.404310528392852\n",
      "Epoch 2011 complete, total errors is 27.484791589513442\n",
      "Epoch 2012 complete, total errors is 26.317122868589678\n",
      "Epoch 2013 complete, total errors is 27.55271415785923\n",
      "Epoch 2014 complete, total errors is 26.45734406681379\n",
      "Epoch 2015 complete, total errors is 26.317363036863288\n",
      "Epoch 2016 complete, total errors is 27.385737317348827\n",
      "Epoch 2017 complete, total errors is 27.452494814921998\n",
      "Epoch 2018 complete, total errors is 27.341146070812755\n",
      "Epoch 2019 complete, total errors is 54.50515102966398\n",
      "Epoch 2020 complete, total errors is 27.43764989791087\n",
      "Epoch 2021 complete, total errors is 27.369398347365966\n",
      "Epoch 2022 complete, total errors is 26.512031521444722\n",
      "Epoch 2023 complete, total errors is 41.06841815005397\n",
      "Epoch 2024 complete, total errors is 26.414572543913508\n",
      "Epoch 2025 complete, total errors is 27.19887144980491\n",
      "Epoch 2026 complete, total errors is 27.33481788246977\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2027 complete, total errors is 27.387992106551593\n",
      "Epoch 2028 complete, total errors is 27.477987712308014\n",
      "Epoch 2029 complete, total errors is 27.454468451150476\n",
      "Epoch 2030 complete, total errors is 27.467846095557633\n",
      "Epoch 2031 complete, total errors is 57.33363919273095\n",
      "Epoch 2032 complete, total errors is 27.57949058791554\n",
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      "Epoch 2035 complete, total errors is 26.44915883673985\n",
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      "Epoch 2037 complete, total errors is 27.49350051028604\n",
      "Epoch 2038 complete, total errors is 27.522728645212197\n",
      "Epoch 2039 complete, total errors is 27.204341352672916\n",
      "Epoch 2040 complete, total errors is 27.500131504605367\n",
      "Epoch 2041 complete, total errors is 27.33621821948993\n",
      "Epoch 2042 complete, total errors is 27.403170649853855\n",
      "Epoch 2043 complete, total errors is 30.227574505379543\n",
      "Epoch 2044 complete, total errors is 27.500664048958964\n",
      "Epoch 2045 complete, total errors is 27.363852426631535\n",
      "Epoch 2046 complete, total errors is 27.441476190267636\n",
      "Epoch 2047 complete, total errors is 27.4345876261946\n",
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      "Epoch 2049 complete, total errors is 27.26193954359536\n",
      "Epoch 2050 complete, total errors is 27.817615372879114\n",
      "Epoch 2051 complete, total errors is 27.521956885997927\n",
      "Epoch 2052 complete, total errors is 27.252532844834533\n",
      "Epoch 2053 complete, total errors is 27.531356948394887\n",
      "Epoch 2054 complete, total errors is 26.480650559595013\n",
      "Epoch 2055 complete, total errors is 52.07105412744332\n",
      "Epoch 2056 complete, total errors is 53.95636163995975\n",
      "Epoch 2057 complete, total errors is 27.622879200144098\n",
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      "Epoch 2060 complete, total errors is 27.40013809346603\n",
      "Epoch 2061 complete, total errors is 27.557794771666703\n",
      "Epoch 2062 complete, total errors is 27.690196371702257\n",
      "Epoch 2063 complete, total errors is 27.543479916247986\n",
      "Epoch 2064 complete, total errors is 27.46198628114298\n",
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      "Epoch 2066 complete, total errors is 27.56576509206027\n",
      "Epoch 2067 complete, total errors is 27.447633229922246\n",
      "Epoch 2068 complete, total errors is 27.257037908450826\n",
      "Epoch 2069 complete, total errors is 27.042234316430523\n",
      "Epoch 2070 complete, total errors is 27.62844424348021\n",
      "Epoch 2071 complete, total errors is 27.48321029164192\n",
      "Epoch 2072 complete, total errors is 27.140440469785506\n",
      "Epoch 2073 complete, total errors is 35.03519920008735\n",
      "Epoch 2074 complete, total errors is 34.96558088282295\n",
      "Epoch 2075 complete, total errors is 37.750959636028405\n",
      "Epoch 2076 complete, total errors is 27.454419673892428\n",
      "Epoch 2077 complete, total errors is 27.372811790306923\n",
      "Epoch 2078 complete, total errors is 27.629079852090467\n",
      "Epoch 2079 complete, total errors is 27.40920670895037\n",
      "Epoch 2080 complete, total errors is 27.651132202148\n",
      "Epoch 2081 complete, total errors is 27.264950432966664\n",
      "Epoch 2082 complete, total errors is 57.763530334704136\n",
      "Epoch 2083 complete, total errors is 46.5449581062592\n",
      "Epoch 2084 complete, total errors is 55.342692785332346\n",
      "Epoch 2085 complete, total errors is 27.358770377302054\n",
      "Epoch 2086 complete, total errors is 26.496555799880255\n",
      "Epoch 2087 complete, total errors is 27.616328601501067\n",
      "Epoch 2088 complete, total errors is 30.39871685937828\n",
      "Epoch 2089 complete, total errors is 27.289644713706267\n",
      "Epoch 2090 complete, total errors is 27.00315828835811\n",
      "Epoch 2091 complete, total errors is 27.572805708357063\n",
      "Epoch 2092 complete, total errors is 27.42805679847046\n",
      "Epoch 2093 complete, total errors is 27.589782420924593\n",
      "Epoch 2094 complete, total errors is 27.655979569812548\n",
      "Epoch 2095 complete, total errors is 56.5233646665346\n",
      "Epoch 2096 complete, total errors is 55.13462059313915\n",
      "Epoch 2097 complete, total errors is 26.729564534909734\n",
      "Epoch 2098 complete, total errors is 27.570509252565895\n",
      "Epoch 2099 complete, total errors is 44.357651957100884\n",
      "Epoch 2100 complete, total errors is 27.16845364838312\n",
      "Epoch 2101 complete, total errors is 27.039924498682403\n",
      "Epoch 2102 complete, total errors is 27.606723986906342\n",
      "Epoch 2103 complete, total errors is 27.230124718703507\n",
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      "Epoch 2107 complete, total errors is 27.309129714304976\n",
      "Epoch 2108 complete, total errors is 27.409256408688396\n",
      "Epoch 2109 complete, total errors is 27.443877180805252\n",
      "Epoch 2110 complete, total errors is 27.552054381586025\n",
      "Epoch 2111 complete, total errors is 57.487062411826706\n",
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      "Epoch 2113 complete, total errors is 27.128939558950947\n",
      "Epoch 2114 complete, total errors is 55.51279905710685\n",
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      "Epoch 2120 complete, total errors is 27.369779164482463\n",
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      "Epoch 2137 complete, total errors is 27.363769962168956\n",
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      "Epoch 2139 complete, total errors is 26.781463432229614\n",
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      "Epoch 2210 complete, total errors is 26.76035367073223\n",
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      "Epoch 2212 complete, total errors is 49.86988186274847\n",
      "Epoch 2213 complete, total errors is 27.648857047022926\n",
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      "Epoch 2216 complete, total errors is 26.39729990021429\n",
      "Epoch 2217 complete, total errors is 27.473570891784078\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2218 complete, total errors is 27.36084738803946\n",
      "Epoch 2219 complete, total errors is 27.477991157463826\n",
      "Epoch 2220 complete, total errors is 57.457451648256296\n",
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      "Epoch 2251 complete, total errors is 27.64827872213744\n",
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      "Epoch 2257 complete, total errors is 41.74631774978833\n",
      "Epoch 2258 complete, total errors is 27.478940823216853\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2400 complete, total errors is 26.317749461721533\n",
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     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2553 complete, total errors is 27.424617537233814\n",
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      "Epoch 2728 complete, total errors is 27.705771721374234\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2729 complete, total errors is 36.190629972209685\n",
      "Epoch 2730 complete, total errors is 27.494322081542666\n",
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      "Epoch 2876 complete, total errors is 57.177323002038676\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 2877 complete, total errors is 26.505843256078833\n",
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      "Epoch 2924 complete, total errors is 27.40660868938437\n",
      "Epoch 2925 complete, total errors is 27.559032238865996\n",
      "Epoch 2926 complete, total errors is 27.44424135341415\n",
      "Epoch 2927 complete, total errors is 27.4644182164542\n",
      "Epoch 2928 complete, total errors is 27.735436222200377\n",
      "Epoch 2929 complete, total errors is 27.49803005806647\n",
      "Epoch 2930 complete, total errors is 27.532017332375176\n",
      "Epoch 2931 complete, total errors is 46.76660627586718\n",
      "Epoch 2932 complete, total errors is 26.459320042733438\n",
      "Epoch 2933 complete, total errors is 26.38492662445106\n",
      "Epoch 2934 complete, total errors is 26.307318950593\n",
      "Epoch 2935 complete, total errors is 27.516304247987648\n",
      "Epoch 2936 complete, total errors is 36.26371054729347\n",
      "Epoch 2937 complete, total errors is 27.26038063095654\n",
      "Epoch 2938 complete, total errors is 27.24698806881659\n",
      "Epoch 2939 complete, total errors is 26.502163024822075\n",
      "Epoch 2940 complete, total errors is 27.5355801296433\n",
      "Epoch 2941 complete, total errors is 27.27645982093877\n",
      "Epoch 2942 complete, total errors is 27.681174164278378\n",
      "Epoch 2943 complete, total errors is 27.505350561521677\n",
      "Epoch 2944 complete, total errors is 27.14837944282862\n",
      "Epoch 2945 complete, total errors is 27.56202659047227\n",
      "Epoch 2946 complete, total errors is 27.577026908707282\n",
      "Epoch 2947 complete, total errors is 27.441592895636852\n",
      "Epoch 2948 complete, total errors is 27.554638019661223\n",
      "Epoch 2949 complete, total errors is 27.47751228209045\n",
      "Epoch 2950 complete, total errors is 27.290354223664885\n",
      "Epoch 2951 complete, total errors is 27.568738914469918\n",
      "Epoch 2952 complete, total errors is 27.659317436749937\n",
      "Epoch 2953 complete, total errors is 52.756837978798615\n",
      "Epoch 2954 complete, total errors is 59.98144650097872\n",
      "Epoch 2955 complete, total errors is 27.552018069303948\n",
      "Epoch 2956 complete, total errors is 27.381396580707595\n",
      "Epoch 2957 complete, total errors is 27.608329174230896\n",
      "Epoch 2958 complete, total errors is 26.92616081783133\n",
      "Epoch 2959 complete, total errors is 26.324861761989453\n",
      "Epoch 2960 complete, total errors is 27.47312657745723\n",
      "Epoch 2961 complete, total errors is 27.4688336771143\n",
      "Epoch 2962 complete, total errors is 27.47514714250061\n",
      "Epoch 2963 complete, total errors is 26.316247597366733\n",
      "Epoch 2964 complete, total errors is 60.02256670334705\n",
      "Epoch 2965 complete, total errors is 27.880702886246905\n",
      "Epoch 2966 complete, total errors is 27.794900517599906\n",
      "Epoch 2967 complete, total errors is 27.29360733240587\n",
      "Epoch 2968 complete, total errors is 27.4178546510359\n",
      "Epoch 2969 complete, total errors is 43.21115784468047\n",
      "Epoch 2970 complete, total errors is 32.861691722103885\n",
      "Epoch 2971 complete, total errors is 27.570124266795165\n",
      "Epoch 2972 complete, total errors is 27.41067190332583\n",
      "Epoch 2973 complete, total errors is 27.497476872910934\n",
      "Epoch 2974 complete, total errors is 27.387652245357824\n",
      "Epoch 2975 complete, total errors is 27.279224948610345\n",
      "Epoch 2976 complete, total errors is 27.434089426753395\n",
      "Epoch 2977 complete, total errors is 27.497945286653565\n",
      "Epoch 2978 complete, total errors is 27.23871335216908\n",
      "Epoch 2979 complete, total errors is 27.368743800464703\n",
      "Epoch 2980 complete, total errors is 27.416558074763984\n",
      "Epoch 2981 complete, total errors is 26.70742466210836\n",
      "Epoch 2982 complete, total errors is 27.58520217804759\n",
      "Epoch 2983 complete, total errors is 27.373357028122495\n",
      "Epoch 2984 complete, total errors is 27.597093920181116\n",
      "Epoch 2985 complete, total errors is 27.461788314591832\n",
      "Epoch 2986 complete, total errors is 27.358205017343217\n",
      "Epoch 2987 complete, total errors is 27.71468161648409\n",
      "Epoch 2988 complete, total errors is 27.346308122840533\n",
      "Epoch 2989 complete, total errors is 26.501629326585125\n",
      "Epoch 2990 complete, total errors is 28.60986203314628\n",
      "Epoch 2991 complete, total errors is 27.677440481291818\n",
      "Epoch 2992 complete, total errors is 27.444777609076503\n",
      "Epoch 2993 complete, total errors is 27.482332291125555\n",
      "Epoch 2994 complete, total errors is 27.569559032887575\n",
      "Epoch 2995 complete, total errors is 27.46361321389861\n",
      "Epoch 2996 complete, total errors is 27.3810268101632\n",
      "Epoch 2997 complete, total errors is 27.584340397347702\n",
      "Epoch 2998 complete, total errors is 27.390390578922066\n",
      "Epoch 2999 complete, total errors is 27.59352214380625\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#创建一个3层的全连接神经网络，每层的神经元个数为 1, 3, 1\n",
    "#其中第一层为输入层，最后一层为输出层\n",
    "network=NeuralNetwork([1,3, 1],sigmoid,sigmoid_derivative,cost_derivative)\n",
    " \n",
    "#训练集样本\n",
    "x = np.array([np.linspace(-7, 7, 200)]).T\n",
    "y = (np.cos(x)+1)/2\n",
    " \n",
    "#使用批量随机梯度下降算法对模型进行训练\n",
    "#迭代288次；每次随机抽取40个样本作为一个batch；学习率设为0.3\n",
    "training_data=[(np.array([x_value]),np.array([y_value])) for x_value,y_value in zip(x,y)]\n",
    "network.SGD(training_data,3000,40,0.3, y)\n",
    " \n",
    "#测试集样本\n",
    "x_test = np.array([np.linspace(-9, 9, 120)])\n",
    "#测试集结果\n",
    "y_predict = network.feedforward(x_test)\n",
    " \n",
    "#图示对比训练集和测试集数据\n",
    "plt.plot(x,y,'r',x_test.T,y_predict.T,'*')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "END"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}